Download Grade 8 Mathematics Arithmatic and Geometric Patterns and

Algebra/Geometry Institute Summer 2003
Lesson Plan Two
Faculty Name: Joanna Dickison
School: Olive Branch Middle School
City: Olive Branch, MS
Grade Level: 8th Grade Math
1
Teaching objective(s)
The students will recognize the difference between arithmetic and geometric patterns, and
create a rule about the sequences.
2
Instructional Activities
v The students will begin class by completing a problem of the day in their journals, where
they will solve the problem and write a paragraph describing the steps they took to find
the solution. Because my school’s schedule is based on a modified block schedule, I
always choose problems that reinforce what the students learned the last time they were
in my classroom (which is 48 hours).
Write on the board (or overhead) the following problem: “Evaluate the
following expression using order of operations, in your journals, then
write a paragraph describing each step and why it was taken.” : 4+23 /2
Once the students have wrapped up their thoughts, two may volunteer to share
their findings with the rest of the class. (The correct answer is 8.) (8-10 minutes)
v Begin with the following monologue (or something close to it). “Some people say that
mathematics is the science of patterns. That's not a bad description. Not only do patterns
take many forms over the range of school mathematics, they are also a unifying theme.
Number patterns—such as 3, 6, 9, 12—are familiar to us since they are among the
patterns we first learn as young students. As we advance, we experience number patterns
again through the huge concept of functions in mathematics. Today we will be exploring
arithmetic and geometric patterns.” (1-2 minutes)
v First, the teacher must explain the difference between arithmetic and geometric patterns.
Arithmetic means we are either adding or subtracting in each sequence, and geometric
means we are either multiplying or dividing in the patterns. (2-3 minutes)
v Then provide 8 examples of sequences on the overhead (like 1,6,11,16,21… or
1,2,4,8,16,32…). One by one, ask the class if each pattern is arithmetic or geometric.
Allow volunteers to answer. Then ask if anyone would like to tell what exactly the
sequence is doing. (For example, the first sequence is +5, and the second seque nce is
× 2 .) Allow students to volunteer. Finally, on each problem ask students to predict the
next 2 numbers, and again allow volunteers to answer. (8 minutes)
v Have six work stations available for students to circulate through in groups of three,
recording their answers on a piece of paper on a clipboard. At each station, there should
be a problem for the students to work. (See example below.) The students should
observe a pattern, decide if it is arithmetic or geometric, and label what each pattern is
specifically doing. Finally, they should predict the next two numbers in the sequence.
(20-24 minutes)
v Have students return to their seats and discuss their results before turning them in.
v Assign an activity sheet (either copied from a resource you may already have, from your
textbook, or a sheet you created yourself) with approximately 8 patterns for the students
to analyze in the same manner. I would do four arithmetic and four geometric patterns.
The problems should be in the same format as the ones the students already have
experience with.
3
Materials and Resources
Materials:
Pencil
Paper
Overhead/transparencies
Overhead marker
6 problems for workstations (see attached)
Activity sheet described above (enough for each student to have one)
Clipboard for each group
Resources:
http://askeric.org/cgi-bin/printlessons.cgi/Virtual/Lessons/Mathematics/Patterns/
Various colleagues who modestly chose not to be credited
4
Assessment
The students will complete the activity sheet on their own with at least 70 % accuracy.
Jack and Jill have opened up a new coffee shop, which has a growing reputation for their
wonderful beverages. In fact, 24 customers came in on Monday, 32 customers came in on
Tuesday, and 40 customers came in on Wednesday.
1) Is the pattern of customers arithmetic or geometric?
2) What is the pattern specifically doing?
3) What will the next two numbers in the sequence of customers be?
Mrs. Sacco in the Counseling Office noticed a pattern in the number of new students that came to
our school from month to month. See if you can answer the following questions if the following
is true.
August
2 new students
September
4 new students
October
8 new students
November
16 new students
1) Is the pattern of new students arithmetic or geometric?
2) What is the pattern specifically doing?
3) What will the next two numbers in the sequence of new students be?
Matt was doing some research on the internet about the price of skateboards from a certain
company, and he noticed a pattern. He found that Model A costs $99.50, Model B costs
$124.50, and Model C costs 149.50. Answer the following questions about the pattern Matt
found.
1) Is the pattern of skateboard prices arithmetic or geometric?
2) What is the pattern specifically doing?
3) What will the next two numbers in the sequence of skateboard prices be?
Ian filled a jar with 60 gumballs, and he and his family helped themselves to them whenever they
liked. Ian counted the second day and found 53 gumballs, and on the third day, there where 46
gumballs.
1) Is the pattern of gumballs arithmetic or geometric?
2) What is the pattern specifically doing?
3) How many gumballs will be in the jar on the fourth and fifth days?
The Warriors have really been improving their record over the past 5 years! Five years ago, they
won only 3 games. The next year, they won 6 games, and the next year, they won 18 games!
1) Is the pattern of winning games arithmetic or geometric?
2) What is the pattern specifically doing?
3) How many games did the Warriors win the next year? How about the next year?
What a shame! My favorite singer, Bill Taylor, has really suffered some losses in the past
albums he has recorded. Look at the chart and use the information to answer the following
questions.
Album 1
256 million albums sold
Album 2
64 million albums sold
Album 3
16 million albums sold
1) Is the pattern of album sales arithmetic or geometric?
2) What is the pattern specifically doing?
3) How many albums do you think Album 4 will sell? What about Album 5?